Prime Minister David Cameron has held the door open for a referendum on an elected House of Lords as a parliamentary committee said the public should be given a say.

In a report examining the Government's reform proposals, the committee backed plans for a slimmed-down Upper House made up of 450 members, 80% elected and 20% appointed, each serving a single 15-year term and earning between £40,000-£65,000 a year, but said that the reforms should be put to a referendum.

But the cross-party panel of 26 MPs and peers was deeply split on several fundamental issues, and 12 members signed an alternative report denouncing the Government's draft reform Bill as unworkable and calling for the establishment of a Constitutional Convention to assess the implications of change.

With a Lords reform Bill expected to be a centrepiece of the May 9 Queen's Speech, the scene is now set for months of bitter wrangling.

Liberal Democrats regard reform of the second chamber as a key priority, and Deputy Prime Minister Nick Clegg has dismissed calls for a referendum as a waste of money. But large numbers of Conservative backbenchers are fiercely opposed to the changes, which they fear would put the traditional primacy of the Commons at risk. And the Bill is also expected to face stiff resistance in the House of Lords - potentially forcing ministers to invoke the Parliament Acts to get their way.

Mr Cameron said he is not personally in favour of a national vote on Lords reform as it would be expensive and proposals to overhaul the upper chamber had been included in the manifestos of all three main parties. But he refused to rule out holding a referendum - something which many of his backbenchers are demanding and which Labour leader Ed Miliband supports.

Mr Cameron told BBC Radio 4's Today programme that reforms would go ahead only if all three parties would agree to "work together, rationally, reasonably, sensibly on trying to deliver what I think the British public would see as, not a priority, but a perfectly sensible reform".

For Labour, shadow justice secretary Sadiq Khan welcomed the committee's backing for a referendum, as well as its call for the future relationship between the House of Commons and any new second chamber to be clarified.

The report backed use of the STV system of proportional representation to elect peers, recommending a version used in New South Wales which allows voters not only to rank individual candidates but also to vote by party. And it backed the Government's proposal for the number of Church of England bishops in a partly elected House to be reduced from 26 to 12.

The committee agreed that the new system should be phased in gradually, with 150 members joining at each of the three general election years of 2015, 2020 and 2025. But rather than removing existing life and hereditary peers at the same rate, as the Government proposes, it argued that all those who fail to attend the Lords on fewer than one in three sitting days should be thrown out in 2015, reducing the size of the Upper House from about 800 to fewer than 600 at a stroke.